RE 2: What I mean is that "N-sigma" and local p-value are being used interchangeably, which you can see from this plot. There's no "number ... calculated without including info about any theory/evidence regarding the Higgs boson".
RE 3: The model used to calculate the background are unphysical in the sense that they set the Higgs production cross section to zero without changing anything else. There's no physical Higgsless theory.
RE 4: I was agreeing with you and adding some facts.
RE 3: The model used to calculate the background are unphysical in the sense that they set the Higgs production cross section to zero without changing anything else. There's no physical Higgsless theory.
RE 4: I was agreeing with you and adding some facts.